Final answer:
The equation of the straight line that passes through the points (9, 2) and (3, 5) is found by calculating the slope and then using the point-slope form. The final equation in slope-intercept form is y = -1/2 x + 6.5.
Step-by-step explanation:
To work out an equation of the straight line that passes through the points (9, 2) and (3, 5), we first need to calculate the slope of the line. The slope is defined as the change in y-division by the change in x (commonly expressed as Δy/Δx). Let's use the formula (y2 - y1)/(x2 - x1) to find the slope.
Using the points (9, 2) and (3, 5), we calculate the slope:
m = (5 - 2)/(3 - 9) = 3/(-6) = -1/2
Now that we have the slope, we can use the point-slope form of a line equation, y - y1 = m(x - x1), with m being the slope and (x1, y1) being a point on the line. We can use either of the given points; let's use (9, 2).
y - 2 = (-1/2)(x - 9)
To get the equation in the slope-intercept form, y = mx + b, we distribute the slope and simplify:
y - 2 = -1/2 x + 4.5
Adding 2 to both sides, we get the final equation of the line:
y = -1/2 x + 6.5